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* German Bund yield hits record lows
* Dutch 10-yields negative for first time since 2016
* Trump Mexico tariff news, China PMI raise recession fears (Updates prices, adds quote)
LONDON, May 31 (Reuters) - Germany's 10-year bond yield slid to record lows on Friday, after U.S. President Donald Trump's sudden threat to impose tariffs on Mexican goods sent shock waves through world markets and heightened fears of a global recession.
Seen as unthinkable even a few weeks ago, the relentless fall in yields in what is seen as one of the world's safest assets -- German government debt -- speaks to the scale of pessimism gripping investors.
"The Trump Mexico tariffs surprised me and more so than the escalation in the trade war with China," said Nordea chief market strategist Jan von Gerich. "This news is negative for markets and the economic outlook."
The global outlook darkened further and a rally in so-called safe assets -- government bonds, yen and gold -- accelerated after a measure of Chinese manufacturing activity in May disappointed.
Dovish comments from the U.S. Federal Reserve's Richard Clarida, saying the Fed would act if inflation stays too low or global risks endanger the economic outlook, only added to a sense that a U.S. rate cut may come sooner rather than later.
Germany's 10-year bond fell more than three basis points to a record low of minus 0.21%. It surpassed a previous all-time low hit in July 2016 just after Britain voted to leave the European Union.
The yield is down more than 20 basis points this month.
"Bund yields are at historic lows even as there are no real rate cuts priced in the euro area," said Rishi Mishra, interest rates strategist at Futures First Info Services.
"It's either the biggest mispricing of the century, or Bund yields are headed below minus 50 bps."
Data showing annual inflation in Germany eased sharply in May reinforced expectations for lower bond yields.
Yields on Dutch 10-year bonds fell below 0% for the first time since 2016.
French 10-year bond yields hit their lowest since 2016 at just 0.21% and Spanish and Portuguese yields hit fresh record lows .
Greece's 10-year bond yield fell below 3% for the first time , putting it on track for its biggest weekly fall since December 2017.
"We have a market that is increasingly concerned about what the future holds for the government of Italy...and the backdrop in Greece is one where the government..has made some notable structural reforms and improved the debt to GDP," said Matt Cairns, rates strategist at Rabobank.
The latest moves will have added to the pool of euro zone bonds carrying sub-zero yields. This amounted to 3.71 trillion euros by close of trade on Thursday, according to Tradeweb, a sharp rise from 3.44 trillion in April.
Worldwide, analysts reckon more than $10.5 trillion in bonds now carry negative yields.
"We have to repeat the old saying that the trend is your friend," DZ Bank strategist Christian Lenk said.
U.S. Treasury yields are not in negative territory but they too resumed their slide, with 10-year yields falling to new 20-month lows.
The U.S. yield curve, as measured in the gap between three-month and 10-year bond yields , was at its most inverted since 2007 in a sign of growing investor concern about recession risks.
And in Britain, 10-year gilt yields fell to their lowest since October 2016 at 0.85%.
Elsewhere in the euro zone, Italian yields jumped in response to the selloff in riskier assets, and growing concerns about the policies of the government in Rome.
Italy's government has no plans to issue small denomination bonds to help pay state debts owed to companies, the Treasury said, looking to quell market concerns about the introduction of a parallel currency.
The so-called "mini-BOT" scheme, named after Italy's Treasury bills, was drawn up by the ruling League party, and on Tuesday parliament approved a motion saying it should be considered.
Two-year Italian yields were up as much as 15 bps at 0.821% but pulled back as trading worse on to 0.70%. Having also risen, long-dated Italian bond yields fell below Thursday's close late in the session. Its 10-year touched a low of 2.626%.
(Reporting by Dhara Ranasinghe and Virginia Furness, Editing by Susan Fenton, Alison Williams and Frances Kerry)